Methods for calculating errors of a function whose arguments have individual errors.

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How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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3answers
64 views

Variance of an average of random variables

This seems like it should be a pretty common problem. I have four estimates of fishing effort, each with its own variance. For subsequent calculations, I want the mean of the four estimates, and a ...
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1answer
51 views

Are the parameters of Non-linear regression independent of each other?

I'm propagating error in the parameters determined by the following growth function... $$ \hat{y} = ae^\frac{t}{b} + (1- a)e^\frac{t}{c} $$ Say I have another model that uses the parameters {a,b,c} ...
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8 views

Backpropagation with Cross-entropy Cost Function

I'm using the cross-entropy cost function for backpropagation in a neutral network as it is discussed here: ...
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1answer
26 views

Cross-entropy Cost Function in Neural Network

I'm looking at the cost function found here: http://neuralnetworksanddeeplearning.com/chap3.html#introducing_the_cross-entropy_cost_function What are we summing over in: C= −1/n ∑x ...
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1answer
24 views

Error propagation and relative error

Say I have measured the value A = 50 +- 2 and from this I am calculating the value: B(A) = A^2 From what I understand I calculate the new error using error propagation to be delta_B ...
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17 views

How to consider propagated measurement errors and “statistical errors”

I come from an Engineering background, and I am familiar with some basics of error treatment. However, discussing with a friend over some data he had to analyze, we couldn't quite figure out what to ...
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11 views

Representing error when there are multiple different, linked error sources

Suppose I make some measurements of variable $X_i$ in separate experiments, and each has some error. In a separate (single) experiment I measure $b$ which is independent of $X_i$ but shared between. ...
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23 views

What is the correct way to interpolate error?

If I have a 2-D data, say $y = f(x)$, with error in the dependent variable, $\delta y$ in this case, and I want to interpolate this data set to a coarser independent variable grid, $x$, what is the ...
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25 views

Adding numbers with asymmetric uncertainties

I need to add a series of numbers with asymmetric standard deviations, such as $$5_{-2}^{+1} \,+ \,3_{-3}^{+1}.$$ Although I know it's common to add the upper errors ($\sigma_{\scriptsize{+}}$) and ...
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19 views

Propagation of uncertainties in functions not continuously differentiable

According to the Guide to the Expression of Uncertainty in Measurement as published by the Bureau International des Poids et Mesures (BIPM), the combined standard uncertainty $u_c^2$ for a function $y ...
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1answer
54 views

Disadvantages of uncertainty in modeling

I am preparing a presentation, my work mainly concentrates on uncertainty and sensitivity analysis. I was wondering if I can convince my audience by the importance of studying uncertainty in modeling. ...
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15 views

Back propagation of Uncertainty

I am recently working on the subject of uncertainty. I read that uncertainty analysis and sensitivity analysis are important topics in this domain(the first is ti do a forward propagation of ...
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0answers
23 views

How would I average noisy data representing the noise using error bars?

I have data that was binned in a process that provides the average and standard deviation for the values in each bin. For some of the data, the variation between bins is significantly larger than the ...
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0answers
38 views

Uncertainty of sum of values estimated through linear regression

I have a continuous record of a variable X, which I want to use as a surrogate for another system value Y. I have a number of measurements of Y, which I can plot against concurrent measurements of X ...
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1answer
20 views

Propagating RMSECV?

I have two regression models, each of which has an associated root mean squared error of cross validation (RMSECV). I would like to combine the results of the models using a weighted average to get a ...
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1answer
41 views

Backward propagation algorithm demonstration in neural networks: any VERY-SMALL-STEP by VERY-SMALL-STEP demonstration?

I'm looking for a VERY DETAILED demonstration for the backward propagation algorithm in neural networks machine learning. Specifically the step below. I've got the excellent Michael Nielsen ...
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18 views

backpropagation: why find the global minimum instead of the value of zero

in back propagation, you use gradient descent to find the stationary point on the equation of the Error = (in terms of weight). But don't we want the error to be equal to zero? if the error is zero, ...
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1answer
19 views

Gini index on data with error margins

I have data series and I want to calculate Gini coefficients for each row as an estimate of matrix sparsity. Hoever values contained in the rows are not exact and have error bounds. My question is ...
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20 views

Error propagation and Standard Deviation

I never quite got the hang of this during my entry stat course and it has been bugging me for a long time now. Lets assume I'm trying to find the focal length of a concave lens. Using a mockup ...
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52 views

Propagation of uncertainty (intersection of two graphs)

The situation is as follows: I performed necessary measurements and used them to create two graphs. I used polynomial regression to find the point of intersection. What I know: precision of ...
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0answers
48 views

Trying to impelement IRPROP+

I'm stuck I tried 3 times to setup IPROP+. I figured IPROP+ was the most highly rated of the three found here http://heatonresearch.com/wiki/RPROP Problem is... my training doesn't seem to work. ...
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146 views

Entropy, Softmax and the derivative term in Backpropagation

I'm currently interested in using Cross Entropy Error when performing the BackPropagation algorithm for classification, where I use the Softmax Activation Function in my output layer. From what I ...
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48 views

Propogation of error in a matrix inversion

I'm trying to find the deterministic error bounds for some parameters calculated through distance geometry. The equation can be simplified to the following form: $ \left[\begin{matrix} x_1 \\ x_2 \\ ...
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1answer
28 views

The probability of m out of K things being wrong with an error of ɛ

I have a homework question about a machine-learning algorithm that uses ensemble learning with simple majority voting. Assuming we have K hypotheses, each with an error ɛ, the question asks us to ...
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1answer
70 views

What does correlation mean in error propagation?

From the python uncertainties package: Correlations between expressions are correctly taken into account. Thus, x-x is exactly zero, for instance (most implementations found on the web yield a ...
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1answer
52 views

Error propagation - nonnormal (again)

I have a dataset of ~2000 points. Each of those points has a standard error value associated with it, and it is assumed that the data points and errors are uncorrelated. Both the dataset and the ...
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47 views

Error propagation through convolution

I have a list of data points $y_i$ and a respective uncertainty $\sigma_i$ associated to them. Now I am convoluting this with a Gaussian window function (discretized $w_i$) "numpy.convolve" function ...
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31 views

Error propagation with the bootstrap method

I am trying to estimate the value of a function (essentially a standard deviation) from a series of experimental data. The value, v, is broadly given by $$ v = \sigma(F(\textbf{x}),F(\textbf{y}), ...
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64 views

propagation of standard error in a sum of proportions

I am new to error propagation, and I am trying to solve a simple problem: I am trying to calculate the estimate and standard error of a parameter (carbon density) across a landscape composed of ...
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45 views

propagation of the error in the summation

I have a question regarding the propagation of the error during the summation. Please see the equation below. In this equation only quantity R has an error. How it will propagate to the final value ...
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36 views

Error propagation and p value

Say I have parameters $a(x$) and $b(x)$, with $N_a(x)$ and $N_b(x)$ experimental measurement counts, respectively. $x$ is an independent variable ($x_1, x_2, ...$). For each $a$ and $b$, I can ...
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28 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
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64 views

time-series forecasting - predicting av. error intervals

I should start with the disclaimer I'm not proficient with R or heavier statistical terminology, sadly! Nevertheless I create sales forecasts (using different methods such as holt-winters), and I'm ...
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22 views

Tools for determining final error with mixture of correlated and independent sources of error

Preface: Not looking for an answer, but rather seeking an approach or set of approaches to deal with a complicated problem. Brief version: I have a single, analytical set of 3 equations with 8 ...
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27 views

How to properly consider uncertainty propagation in random variables

I have 34 input random variables and one output random variable, named R. From 33 input random variables and some dataset I determined the best predictive ...
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2answers
362 views

Background subtraction for signal and error analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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2answers
241 views

Error for combining multiple binomial distributions

This problem is somewhat involved and I have a partial solution so bear with me. I will illustrate the problem with an example. Lets say we have two processes and we want to know which has a higher ...
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99 views

Propagation of Poisson Confidence Intervals

I have a set of measurement with 95% Poisson confidence intervals, and I would like to subtract and multiply them and propagate the error. For example, I measured the copy number of a piece of DNA in ...
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1k views

Standard deviation of normalized data

I have a data set $y_i$ (where the $y_i$ are photon counts in time period $i$, $i=1,2,...,n$, assumed Poisson), with an estimated standard error $s_i$ (= $\sqrt{y_i}$) for each count. For some ...
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1answer
53 views

Error Propagation Calculation

I have a few machines that are used to calibrate each other. Machine 1 has is accurate to 0.025% Machine 1 is used to calibrate Machine 2, which has an accuracy of 0.005% Machine 2 is used to ...
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77 views

How do I propagate error when X+Y=1 and aX+bY=1?

I have data for proportions of two diet categories X and Y (from gut samples, n=10) that must sum to 1. I am multiplying each by a different constant (a and b) and then re-calculating the two ...
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2answers
86 views

Statistical error and error propagation

I have a quantity defined as: $P_{frac} = \frac{F_{max}-F_{min}}{F_{max}+F_{min}}$ I also have the value for $F_{max}$, $F_{min}$, and their statistical errors. How can I calculate the error for ...
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0answers
183 views

Error propagation calculation yielding negative variance

I am trying to calculate the standard deviation of the sum X = A + B. A and B are mean values, and I do not have access to the source data. A is 0.46 with an SD of 0.014 (SDa) and B is 0.375 with an ...
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1answer
166 views

How to compare two groups of empirical distributions?

I am working with EEG and now I am trying to compare coherence for two groups of individuals. Problem is coherence is dependent on length of signal but I have signals with different length for each ...
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1answer
86 views

Reusing predicted values as independent variables for new linear regression

Edit I've rephrased this question severely. Suppose I have a fitness center, and instead of a monthly fee, the people are paying for courses they are taking. I've got the monthly total revenue of all ...
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1answer
223 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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0answers
58 views

Regression with error in covariates

I am looking for some advice for a colleague who is dealing with regression models for which it is know, that the continuous covariate of interest $X_1$ was measured with error. More precisely, we ...
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1answer
123 views

Possible Paradox: Calculating a confidence interval with within-experiment error

This is a spinoff of How to calculate the confidence interval of the mean of means? and related to When making inferences about group means, are credible Intervals sensitive to within-subject ...
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1answer
593 views

When making inferences about group means, are credible Intervals sensitive to within-subject variance while confidence intervals are not?

This is a spin off of this question: How to compare two groups with multiple measurements for each individual with R? In the answers there (if I understood correctly) I learned that within-subject ...